For this test I have two basic builds: One soft caps Magicka and overcharges Spell Power by 4%, while the other soft caps Stamina and overcharges Weapon Damage by 14%. I also have a typical "balanced" Stamina build here that has a fairly even split of Magicka/Stamina and Spell Power/Weapon Damage, which represents what most Stamina users have to do in order to avoid destroying the damage of their class skills, which ALL scale off Magicka.
Magicka Build with Restoration Staff:

Magicka: 2398/2383 - Basically soft capped (only 15 over).
Stamina: 1618/2383 - Basically default. The extra 12 from stats is random.
Spell Damage: 128/123 - Overcharged by crafted gear/jewelry. 4% over cap.
Weapon Damage: 125/187 - Baseline from staff.
Soul Harvest IV: 680 base damage.
Veil of Blades IV: 128 damage per tick.
Magicka Build with Destruction Staff:

Magicka: 2398/2383 - Basically soft capped (only 15 over).
Stamina: 1618/2383 - Basically default. The extra 12 from stats is random.
Spell Damage: 128/123 - Overcharged by crafted gear/jewelry. 4% over cap.
Weapon Damage: 125/187 - Baseline from staff.
Soul Harvest IV: 619 base damage.
Veil of Blades IV: 117 damage per tick.
Typical BALANCED Stamina Build with Daggers:

Magicka: 2061/2383 - Balanced with Stamina.
Stamina: 2037/2383 - Balanced with Magicka.
Spell Damage: 120/123 - From crafted jewelry (glyphs) only.
Weapon Damage: 183/187 - From daggers and crafted gear.
Soul Harvest IV: 557 base damage.
Veil of Blades IV: 106 damage per tick.
As you can see here, the typical balanced Stamina build is 12% weaker than the Magicka build with Destruction Staff and 20% weaker than the same Magicka build with a Restoration staff!
OK, but what happens to our Magicka build if we pick up Molten Weapons (+10 Weapon Damage buff)
which puts our weapon damage higher than our spell damage? For Magicka users, NO CHANGE.
It appears the test they use to determine which stat is higher either goes by a PERCENT of the cap, or is broken. Lucky for Magicka users, as even when their Weapon Damage is higher than their Spell Power, their ultimates still scale off their two strongest stats (Spell Power and Magicka).

http://www.youtube.com/watch?v=PfMS13oaD0w
So, lets test it for our Stamina setup, which we KNOW is using Weapon Damage. Molten Weapons puts us over the soft cap for Weapon Damage, so even if going by percents it should make a difference. But, lo and behold, NO CHANGE AT ALL!
http://www.youtube.com/watch?v=bTmaF88yoaA
Sad sad Stamina users.

OK, so what if we start making all our class skills (most of our bar) extremely weak
in order to pump our Stamina further over the soft cap than Magicka was? Will THAT make a difference? Lets test it out.
What I did here, is respec (thank you 4k+ gold for science!) my stats out of Health and Magicka to max out Stamina. I made it so that it is just a little over soft cap just like Magicka in the first test (actually a little MORE over the cap than Magicka was). I also used Power Extraction on my 2nd bar on 3 mobs before swapping back to my empty dagger bar, to massively overcharge my Weapon Damage. Lets look at those numbers:
Tweaked Stamina Build with higher stats than Magicka build:

Magicka: 2072/2383 - From gear and passives.
Stamina: 2405/2383 - Basically soft capped (22 over, more than Magicka was).
Spell Damage: 120/123 - From crafted jewelry (glyphs) only.
Weapon Damage: 213/187 - From daggers, crafted gear, and Power Extraction.
(14% over cap. Almost 4x more over the cap than Spell Power was.)
Soul Harvest IV: 591 base damage.
Veil of Blades IV: 115 damage per tick.
Since our Stamina is overcharged more than our Magicka was for our magic test, and our Weapon Damage is WAY more overcharged than our Spell Power was,
you would expect some really nice numbers on our ultimates, right? WRONG!Still over 2-5% weaker than our Destruction Staff Magicka build with far weaker stats, and 12-15% weaker than with a Restoration Staff on that same lower stat Magicka build!
Additionally, that is after completely ruining the damage of the 60% or more of our bar that are class skills just to cap Stamina, leaving us doing far less damage overall just for ultimates that are STILL weaker!
What the hell, ZOS?